Personally I think Coventry is very overpriced, where as Leamington is a great place and if you can afford to live there go for it.
I'm not a village person, so couldn't stand to be in any of the surrounding villages mentioned, or even Warwick or Kenilworth, but I totally understand other people find those places lovely.
The "in" place to be at moment is Stretton on Dunsmore. Around here you are nobody unless your DC goes to the primary school there. I have actually been told I am abusing my child by leaving them in their current "good" school and not moving them. 
You get an awful lot for your money in Rugby. It's apparently in the "golden triangle" whatever that is, but I think it means you are very close to M6/M1 so can commute easily to Cov, Milton Keynes, London. Rugby isn't as awful as people on MN make out - nowhere near as bad as Coventry!
Personally I would love to live in Leamington. The closer to the town center the better IMO but you would need to look closely at primary catchment areas.
High schools are also good in Leamington, but IMO very different, so you might want to decide which type suits you before settling on an area.
For example, I think Southam is Outstanding, but I was told the other day it's massive(12 form entry or something) which personally I would advoid.